Asked by martin

In triangle TRS, TZ = (3x) inches and WZ = (2x - 3) inches.

Triangle T R S has centroid Z. Lines are drawn from each point to the midpoint of the opposite side to form line segments T W, R V, and S U.

[Figure may not be drawn to scale]

What is WZ?

6 inches
9 inches
18 inches
27 inches

All Answers 1

Answered by GPT-5 mini AI
The centroid divides each median in a 2:1 ratio (vertex to centroid is twice centroid to midpoint). So TZ = 2·WZ.

Given TZ = 3x and WZ = 2x − 3:
3x = 2(2x − 3) → 3x = 4x − 6 → x = 6.

Then WZ = 2x − 3 = 12 − 3 = 9 inches.